{
  "abstract": "FINDING: The A₁ root system (sl(2,C)) is the fundamental Lie-algebraic skeleton of qubit Hilbert space, with its principal elements and embeddings into sl(m,K) revealing universal structural constraints; Malcev algebras and Nichols braided Lie algebras extend this to non-associative and braided quantum symmetries. | MATH: A₁ ≅ sl(2,C) has root system {±α}, Cartan matrix [2], Weyl group ℤ₂; spin-1/2 Hilbert space ℂ² is the fundamental irrep with Pauli generators σ_x, σ_y, σ_z satisfying [σ_i,σ_j]=2iε_ijk σ_k. Frobenius Lie algebra principal element: e = Σ h_i (Cartan subalgebra generator) with semisimple part having eigenvalues related to root values; embedding theorem: any Lie algebra with left-symmetric (pre-Lie) structure embeds into sl(m,K) — for A₁, m=2 gives the qubit. Malcev algebra correspondence: a Lie algebra L(M) uniquely determined by Malcev algebra M, with anti-commutator [x,y] and Jacobiator proportional to associator — for A₁, the Jacobi identity holds trivially. Nichols\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/63rf8ahf0wa41.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587193",
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  "id": "63rf8ahf0wa41",
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  "language": "eng",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/63rf8ahf0wa41.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:51Z",
      "native_id": "23587193",
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      "url": "https://zenodo.org/records/23587193"
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  "subjects": [],
  "title": "A₁ as the Universal Lie-Algebraic Skeleton of Qubit Symmetry — E8 Intelligence Research",
  "title_text": "A₁ as the Universal Lie-Algebraic Skeleton of Qubit Symmetry — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:51Z",
  "url": "https://research.draconitic.com/paper/63rf8ahf0wa41",
  "venue": "Zenodo",
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}